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We investigate different mechanisms for the control of directed transport of particles on two-dimensional periodic and symmetric substrates, based on the application of a crossed static and a bi-harmonic (harmonic mixing) field. We focus on inertial systems in the low friction regime, using a prototypical model for atom-surface diffusion, and demonstrate that a proper control of current reversals can be achieved at moderate field strengths by tuning either the static field or changing the relative phase of the harmonic mixing signal, respectively.